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Metallic Contact Contributions in Thermal Hall Conductivity Measurements

Hongyu Ma, Xuesong Hu, Junren Shi

TL;DR

The paper addresses how metallic contacts can generate spurious thermal Hall signals in measurements of the thermal Hall effect by bypassing heat flow and creating a transverse temperature gradient under a magnetic field. It develops analytic and finite-element models for electrode and wire contacts, deriving an apparent $\kappa_{xy}^{\mathrm{app.}}$ and a geometry correction factor $\delta$ that depends on contact geometry and material properties, and then fits data from diverse materials under the assumption of zero intrinsic $\kappa_{xy}$ to estimate contact influence. The key finding is that modest contact thicknesses relative to sample width (roughly $t/W \sim 10^{-2}$ to a few $\times 10^{-2}$) with silver-like conductivity can reproduce the observed $\kappa_{xy}$ trends across materials, especially when accounting for geometric corrections; this underscores the importance of accounting for contact artifacts in THE measurements and motivates a long-arm, low-leakage measurement geometry to suppress these effects. The work provides practical guidance for designing experiments to minimize contact-induced artifacts, thereby improving the reliability of THE signals used to probe neutral heat carriers.

Abstract

We investigate the influence of metallic contacts on thermal Hall measurements. By analyzing typical measurement setups, we show that heat currents bypassing through metallic contacts could generate non-negligible thermal Hall signals. We find that contributions from metallic contacts with thicknesses on the order of 10$^{-2}$ of sample widths can approximately replicate experimental observations across different materials in both temperature dependence and magnitude, assuming silver contacts with a conductivity of $10^{8}~\mathrm{S/m}$. Our analysis underscores the need to minimize metallic contact effects in thermal Hall measurements, which can be achieved by optimizing measurement configurations.

Metallic Contact Contributions in Thermal Hall Conductivity Measurements

TL;DR

The paper addresses how metallic contacts can generate spurious thermal Hall signals in measurements of the thermal Hall effect by bypassing heat flow and creating a transverse temperature gradient under a magnetic field. It develops analytic and finite-element models for electrode and wire contacts, deriving an apparent and a geometry correction factor that depends on contact geometry and material properties, and then fits data from diverse materials under the assumption of zero intrinsic to estimate contact influence. The key finding is that modest contact thicknesses relative to sample width (roughly to a few ) with silver-like conductivity can reproduce the observed trends across materials, especially when accounting for geometric corrections; this underscores the importance of accounting for contact artifacts in THE measurements and motivates a long-arm, low-leakage measurement geometry to suppress these effects. The work provides practical guidance for designing experiments to minimize contact-induced artifacts, thereby improving the reliability of THE signals used to probe neutral heat carriers.

Abstract

We investigate the influence of metallic contacts on thermal Hall measurements. By analyzing typical measurement setups, we show that heat currents bypassing through metallic contacts could generate non-negligible thermal Hall signals. We find that contributions from metallic contacts with thicknesses on the order of 10 of sample widths can approximately replicate experimental observations across different materials in both temperature dependence and magnitude, assuming silver contacts with a conductivity of . Our analysis underscores the need to minimize metallic contact effects in thermal Hall measurements, which can be achieved by optimizing measurement configurations.

Paper Structure

This paper contains 7 sections, 11 equations, 6 figures.

Table of Contents

  1. introduction
  2. Metallic contact contributions
  3. Fit to experimental results
  4. Summary and Discussion
  5. Heat current distribution in a wire
  6. Geometric correction
  7. Influences of silver paint and thermal boundary resistance

Figures (6)

  • Figure 1: Simplified schematics of THE measurement configurations. (a) Electrode configuration: The red regions represent metallic electrodes with thickness $t$ and length $l_{c} \gg t$. The blue region represents the sample to be measured, with width $W$ and length $L$. Arrowed lines illustrate the heat current through the system and diverting into the electrodes. (b) Wire configuration: The red regions represent metallic wires with a diameter $d$.
  • Figure 2: Fits to experimental thermal Hall conductivity ($\kappa_{xy}^{\mathrm{exp.}}$) for (a) SrTiO$_3$PhysRevLett.124.105901, (b) Nd$_2$CuO$_4$boulanger2020thermal, (c) Cu$_3$TeO$_6$chen2022large, (d) SrTiO$_3$jin2024discovery, (e) SiO$_2$jin2024discovery and (f) Y$_2$Ti$_2$O$_7$PhysRevB.110.L100301. Experimental longitudinal thermal conductivities ($\kappa_{xx}^{\mathrm{exp.}}$) reported alongside $\kappa_{xy}^{\mathrm{exp.}}$ are also shown. Solid curves show fits to $\kappa_{xy}^{\mathrm{exp.}}$, with ($\kappa_{xy}^{\mathrm{app.}}\cdot \delta$) and without ($\kappa_{xy}^{\mathrm{app.}}$) the geometric correction, using Eq. \ref{['eq:kmdelta']} and Eq. \ref{['eq.1']}, respectively. For geometric corrections, contact configurations specified in experiments are utilized: (a) uses the electrode configuration, assuming $t/l_{c}=1/20$, (b)--(f) use the wire configuration ($t/l_{c} = \infty$). Numbers adjacent to the legends indicate the $W/t$ values used for fitting.
  • Figure 3: Same as Fig. \ref{['fig.2']} but for (a) La$_2$CuO$_4$boulanger2020thermal and (b) Sr$_2$CuO$_2$Cl$_2$boulanger2020thermal. Arrows indicate the peak positions of $\kappa_{xx}^{\mathrm{exp.}}$ and $\kappa_{xy}^{\mathrm{exp.}}$. The wire configuration is assumed when determining geometric corrections.
  • Figure 4: A sample shape designed to minimize the influence of metallic components in THE measurements.
  • Figure 5: Geometric correction factor $\delta$ as a function of $\kappa_{xx}/\kappa_{xx}^\mathrm{c}$ and geometric ratio $t/l_{c}$. Points represent numerical results, while curves show values yielded by the Padé formula Eq. \ref{['eq:pade']}. The wire configuration corresponds to $t/l_{c} \rightarrow \infty$.
  • ...and 1 more figures